Device and method for converting an optical frequency

ABSTRACT

To optimise the transformation rate (efficiency) in the optical frequency conversion of laser beams of ultra-short light pulses in optically non-linear media such as a crystal ( 56 ), a double refracting crystal ( 54 ) is arranged in the beam path before the optically non-linear medium ( 56 ). The length of the double refracting crystal ( 54 ) is selected and the orientation of its optical crystal axis in relation to the propagation direction of the laser beams involved in the frequency conversion is set such that the change caused by the double refracting crystal ( 54 ) in the location, time and direction of incidence of the laser pulses ( 14 ) and ( 16 ) on the optically non-linear medium ( 56 ) and the resulting change in the spatial and temporal overlap of the laser pulses in the optically non-linear medium ( 56 ) for optical frequency conversion in the crystal ( 56 ) give a conversion efficiency which is higher than the conversion efficiency which would be achieved without the double refracting crystal ( 54 ).

[0001] The invention concerns a device for optical frequency conversionaccording to the preamble of claim 1, a method for optical frequencyconversion according to the preamble of claim 10, and the use of adouble refracting crystal to optimise an optical frequency conversion inat least one optically non-linear medium.

[0002] The optically non-linear frequency conversion of laser beams is aknown process for generating from laser light of frequency ω, laserlight with a different frequency. Examples of optically non-linearfrequency conversion are three-wave mixed processes such as sumfrequency mixing (SFM), frequency doubling (SHG), difference frequencygeneration (DFG) and optically parametric oscillation (OPO). The mediumin which the frequency conversion takes place is usually an opticallynon-linear crystal. One important parameter in all optically non-linearprocesses is the transformation rate (efficiency). The transformationrate indicates how much of the beam power irradiated into the opticallynon-linear crystal is transformed by the optically non-linear processinto the beam power of the frequency-converted beam. Usually as high aspossible a transformation rate is desired. In order to achieve a highertransformation rate with the optically non-linear method, a good spatialoverlap of the interacting beams in the non-linear medium is necessary.If the laser beam consists of light pulses, the transformation rate isaffected not only by the spatial overlap but also by the temporaloverlap of the interacting light pulses. Only if the pulses pass throughthe optically non-linear crystal at the same time is there optimuminteraction. This should be noted in particular for ultra-short laserpulses. Ultra-short pulses are pulses with a duration of typically lessthan 100 ps and preferably less than 10 ps. The short duration of thesepulses leads to the temporal overlap of the interacting pulses oftenbeing reduced, as for example only a part (e.g. the front flank) of thepulse of the one beam overlaps with a part (e.g. the back flank) of thepulse of the other beam. This gives a temporal overlap which is lessthan a temporal overlap arising if the pulse maxima reach the same placein the crystal at the same time and move through this with the samespeed. With such a complete temporal pulse overlap the transformationrate is usually maximum.

[0003] A temporal delay in pulses in an optically non-linear crystalarises from the dependency of the refractive index on the wavelength(dispersion). If two ultra-short pulses of different wavelength passthrough a dispersive medium, the pulses are moved apart temporally. Thedecisive physical parameter for the propagation speed is the groupspeed. This can be calculated from the refractive index (n) and thechange in refractive index with wavelength (λ). The different groupspeeds of laser pulses with different wavelength and/or polarisationlead to a different temporal delay in comparison with propagation in avacuum and hence may lead to a non-optimum temporal overlap of thepulses in the non-linear crystal, whereby the non-linear interactionbetween the pulses is reduced and hence the transformation rate reduced.To calculate the temporal delay of ultra-short pulses, the decisivefactor is not calculation of the delay via the difference in opticalpaths (n.L) but the distance L which must be travelled at group speedv_(gr) of the light pulse. The group speeds are calculated using thedispersion formulae with the relation:$v_{{g\quad r},0} = \left( {\frac{n_{0}}{c} - {\frac{\lambda}{c}\frac{\partial n_{0}}{\partial\lambda}}} \right)^{- 1}$

[0004] for the ordinary refractive indices and via the equation$v_{{g\quad r},e} = \left( {\frac{n_{e}(\theta)}{c} - {\frac{\lambda}{c}{n_{e}(\theta)}^{3}\left( {{\frac{\cos^{2}\theta}{n_{o}^{3}}\frac{\partial n_{0}}{\partial\lambda}} + {\frac{\sin^{2}\theta}{n_{e}^{3}}\frac{\partial n_{e}}{\partial\lambda}}} \right)}} \right)^{- 1}$

[0005] for the extraordinary refractive indices. n₀ and n_(e) are theordinary and extraordinary refractive indices for wavelength λ, n_(e)(2)is the extraordinary refractive index which depends on angle θ betweenthe optical axis of the crystal and the propagation direction of laserbeam.$\frac{\partial n_{o}}{\partial\lambda}\quad {and}\quad \frac{\partial n_{e}}{\partial\lambda}$

[0006] are the derivatives of the ordinary and extraordinary refractiveindices by wavelength, and c is the light speed.

[0007] In the frequency conversion, the phase adaptation condition mustbe fulfilled for efficient generation. The phase adaptation conditioncorresponds to the pulse obtained for the non-linear method. The phaseadaptation condition can for example by fulfilled in double refractingcrystals. The phase adaptation condition is Δk=k₃−k₁−k₂=0, i.e. the wavevectors k₁ and k₂ of the irradiated waves and wave vector k₃ of thegenerated waves must add up to zero.

[0008] In double refracting crystals, the refractive index and hence thelength of the wave vector is dependent on the angle of the propagationdirection of the irradiated light to the optical axis. By irradiatinglaser light with a suitably set angle to the optical axis, the phaseadaptation condition can be fulfilled. In general by irradiating thelaser light with an angle to the optical axis, a walk-off is generated.The walk-off arises from the difference in the direction of the wavevector k (as the normal vector on the wave front) to the direction ofthe energy flow which is described by the Poynting vector. The walk-offangle ρ is calculated as:$\rho = {{\pm {\arctan \left\lbrack {{\left( \frac{n_{0}}{n_{e}} \right)^{2} \cdot \tan}\quad \theta} \right\rbrack}} \mp \theta}$

[0009] The upper prefix in the formula is valid for negative crystalsfor which n₀>n_(e). The lower prefix in the formula is valid forpositive crystals for n_(e)>n₀. Negative and positive crystals here doesnot refer only to uniaxial crystals. The formula is also valid forcalculating the walk-off angle for biaxial crystals if the propagationtakes place in the main planes of the biaxial crystals.

[0010] For optically non-linear frequency conversion, usually opticallynon-linear crystals with double refraction are used. A further class ofoptically non-linear crystals are crystals with quasi phase adaptationin which the non-linear susceptibility is modulated periodically. In adouble refracting crystal the propagation speed of the pulse isdependent on the wavelength and polarisation of the beam. In this wayrun time differences occur between pulses of different polarisation evenif they have the same wavelength.

[0011] On frequency conversion in non-linear crystals with ultra-shortlaser pulses, consequently in general the walk-off leads to a spatialand the run time difference to a temporal offset of the pulses whichleads to a non-optimum overlap of pulses so the conversion efficiency isreduced.

[0012] An improvement in the spatial and temporal overlap is thereforeof essential significance for frequency conversion. Therefore it isimportant to compensate for the spatial walk-off and the run timedifferences by a suitable method in order to improve the spatial andtemporal overlap simultaneously.

[0013] This is particularly important for non-linear frequencyconversion processes which comprise several successive non-linearconversion processes. Examples are frequency tripling in which thefrequency-doubled beam is generated by a first non-linear crystal andthen in a second non-linear crystal the third harmonic is generated asthe sum of frequency-doubled and fundamental laser beams. A furtherexample is the generation of the fifth harmonic of the laser beam inwhich for example, after the frequency tripling in a further non-linearcrystal, the fifth harmonic of the fundamental laser beam is generatedby sum frequency generation of the tripled beam with thefrequency-doubled beam.

[0014] For the frequency conversion in an optically non-linear crystalof two laser beams which are each polarised linear but orthogonal toeach other, for frequency conversion with type II phase adaptation oneof the two beams passes through the crystal as an ordinary wave and theother beam passes through the crystal as an extraordinary wave. Becauseof the different refractive indices and dispersion for ordinary andextraordinary beams, the group speed for the two beams differs. Theresult is a temporal offset of pulses which changes during passagethrough the crystal. In addition the walk-off of the extraordinary beamleads to a spatial offset of the extraordinary beam relative to theordinary beam. Both the run time differences and the walk-off usuallylead to a reduction in conversion efficiency.

THE STATE OF THE ART

[0015] The literature discloses various methods to compensate for thespatial walk-off in frequency conversion. Publication U.S. Pat. No.5,047,668 (“Optical walk-off compensation in critically phase-matchedthree-wave frequency conversion systems”, Bosenberg) specifies a methodin which a pair of optically non-linear crystals for frequencyconversion are arranged so that the orientation of their optical axesrelative to the radiation axis is reversed. This compensates for thespatial separation of ordinary and extraordinary beams from the walk-offof the extraordinary beam in the first crystal by the equivalent mergingof both beams from the walk-off in the reverse-orientated secondcrystal. The result is overall an improved spatial overlap of the beamsand hence a higher conversion efficiency. This method has severaldisadvantages. Two crystals are necessary, both of which must beprecisely controlled to maintain the phase adaptation condition in theangle of the optical axis to the propagation direction of the laserbeam. This is a requirement which in practice can only be achieved atvery high cost, since the necessary precision of the angle adjustment incritically phase-adapted frequency conversion processes is typicallyless than 0.1 degree and also in the optimum configuration two crystalsmust be set with this precision.

[0016] Furthermore in this state of the art compensation for the spatialwalk-off is not complete. To further increase the spatial overlap of thebeams involved, more than two optically non-linear crystals of the sametype must be arranged in periodically successive reverse orientation.

[0017] This is described in the publication “Increased AcceptanceBandwidths in Optical Frequency Conversion by Use of MultipleWalk-off-compensating Non-linear Crystals”, A. V. Smith et al., (J. Opt.Soc. Am. B., vol 15, pp 122-141, 1998). The practicability of such anarrangement is low as the phase adaptation condition must be maintainedfor all crystals. Therefore each individual crystal must be preciselyadjusted in its spatial position and held in this position irrespectiveof environmental influences. Also in such an arrangement the opticallosses increase even if anti-reflection coatings are applied to thecrystal facets. By reflection and absorption losses, in a multiplicityof crystals the efficiency can even be reduced in comparison with atwo-crystal arrangement. The disadvantage is furthermore that the newlygenerated beam must run through all surfaces. In particular for theproduction of ultra-violet (UV) light at high power, problems can arisein respect of interference and hence the life of the surfaces of thenon-linear crystals. The known processes for use of prisms or prism-likechamfered crystal ends to separate the UV beam from the remaining laserbeam and hence to avoid UV-resistant anti-reflection coatings on thecrystal facets, cannot be applied here. A further serious disadvantageof arrangements of 2^(n) frequency conversion crystals (n≧1) is theincreased cost. The costs of optically non-linear crystals are above allthe costs for machining and coating the surfaces i.e. for opticalpolishing and anti-reflection coating of the inlet and outlet surfaces.

[0018] In the device according to the said U.S. Pat. No. 5,047,668(Bosenberg) there is no compensation for run time differences whicharise for pulsed laser beams. The crystals are oriented so that thephase adaptation condition for frequency conversion is fulfilled. Forthis crystal orientation, the dispersion will generally lead to adifference in group speeds of two pulses of different wavelengths and/orpolarisation, so that because of the run time differences of the pulsesin the crystals the conversion efficiency is reduced. U.S. Pat. No.5,047,668 (Bosenberg) contains no teaching on how to set the run timesin order to influence and compensate for the run time differences oflaser pulses in a targeted manner.

[0019] EP 0503875A2 (“Poynting vector walk-off compensation in type IIphase matching”, Nightingale) describes a further method forcompensation for spatial walk-off in optically non-linear crystals. Theangle between the Poynting vectors of the beams concerned is compensatedin the crystal in that the beams are not irradiated into the crystalperpendicular to the surface. By irradiating the laser light at anangle, the beams are broken on the inlet facet of the crystal, thedirection of the wave vectors thus changed. For collinear light beamswhich differ in polarisation and/or wavelength, an angle then arisesbetween the wave vectors in the crystal which, with suitable choicesangle of incidence and orientation of the crystal axes in relation tothe inlet facet of the crystal, compensate for the walk-off anglebetween the Poynting vectors. Compensation of the spatial walk-off heretakes place over the entire crystal length. It is advantageous that onlyone optically non-linear crystal need be used. This method however hasdisadvantages. For a particular frequency conversion process, theirradiation angle and orientation of the optical axis of the crystalsmust be specially adapted. These angles are determined by the wavelengthand polarisation of the irradiated light beams and the refractiveindices of the crystal for these light beams. For this EP 0503875A2(Nightingale) gives a calculation specification. It is shown howeverthat this condition cannot always be fulfilled. In particular tocompensate for greater walk-off angles, the crystal for the light beamsmust have a large double refraction in order to be able to achieve adouble refraction angle which is equal to the walk-off angle. Theprocess of the non-perpendicular irradiation to compensate for walk-offis therefore preferred for small walk-off angles. For frequency doublingin type II phase-adapted KTP with a walk-off angle of 0.2°, Nightingalespecifies an angle of incidence of 7.34°. For the sum frequency mixingof a 1064 nm laser beam with a frequency-doubled 532 nm beam in type IIphase-adapted LBO to generate UV radiation with a wavelength of 355 nm,for the corresponding walk-off angle of 0.5°, an angle of incidence of27° is calculated to compensate for this walk-off in the crystal. Afurther disadvantage is that for frequency doubling with this method,compensation for walk-off is possible only in crystals with type IIphase adaptation. The disadvantage is also that due to thenon-perpendicular irradiation, the beams in the non-linear crystalundergo a change in beam cross section. The beam becomes astigmaticwhereby a reduction in the common overlap occurs. To compensate for theastigmatism, before entry into the non-linear crystal the beams must besuitably formed. For this known methods are available such as the use ofcylinder optics or spherical resonator mirrors with non-perpendicularincidence, which however all entail an increased cost.

[0020] As the arrangement with the non-perpendicular incidencecompensates only for the spatial walk-off, pulses with differentpolarisation and/or wavelength must be shifted temporally in relation toeach other during passage through the optically non-linear crystal.There is no compensation for run time differences and the method giveni.e. the non-perpendicular irradiation into the crystal, cannot achievethis.

[0021] Arrangements to generate higher harmonics of laser light withimproved spatial overlap are disclosed in publications U.S. Pat. No.5,835,513 (“Q-switched laser system providing UV light”, Pieterse etal.) and U.S. Pat. No. 5,848,079 (“Laser with frequency multiplication”,Kortz et al.). In both publications, two optically non-linear crystalsare arranged in succession. The first non-linear crystal is a crystal togenerate the second harmonic, the second non-linear crystal serves as afrequency multiplier. The common factor in both publications is that thefirst non-linear crystal (frequency-doubling crystal) is cut forcritical phase adaptation. Thus in this non-linear crystal a walk-offoccurs between the fundamental laser wave and the second harmonic. Thewalk-off angle is given in U.S. Pat. No. 5,848,079 (Kortz) as 0.1° to6°. In U.S. Pat. No. 5,835,513 (Pieterse) no value is given for thewalk-off angle but the cut angle of the frequency doubler crystal LBOshould be between 5° and 10° for the crystal angle phi and between 85°and 90° for the crystal angle theta. The person skilled in the art cancalculate the walk-off angle from this information.

[0022] The walk-off in the frequency doubler crystal spatially separatesthe beams of the fundamental laser wave and the second harmonic. Thisspatial separation of the fundamental and the harmonic, with anappropriate arrangement of the second optically non-linear crystal,causes an improved spatial overlap therein. The improved spatial overlapleads to an increase in conversion efficiency to generate the thirdharmonic in this second non-linear crystal. The disadvantage in theteaching of U.S. Pat. No. 5,835,513 (Pieterse) and U.S. Pat. No.5,848,079 (Kortz) is that for frequency doubling using the firstnon-linear crystal, an optically non-linear crystal with critical phaseadaptation must be used, since a walk-off can only be generated in thisfrequency doubler with critical phase adaptation. The critical phaseadaptation however has the disadvantage that the conversion efficiencyis generally less in comparison with a non-critical phase adaptationwithout walk-off. The frequency doubling according to U.S. Pat. No.5,835,513 (Pieterse) and U.S. Pat. No. 5,848,079 (Kortz) will thereforegenerate a lower power of the second harmonic, whereby then theconversion efficiency in this second non-linear crystal is also lower. Afurther disadvantage is that the crystal lengths of the frequencydoubler and the second non-linear crystal cannot be selectedindependently of each other in this method as a specific spatialseparation is required between the fundamental wave and the generatedsecond harmonic after the doubler crystal which must be adapted to thewalk-off in the second non-linear crystal and its length. The crystallength of the doubler crystal should be selected accordingly so that thewalk-off in the second non-linear crystal is compensated. Only then willthere be a sunstantially improved spatial overlap in the secondnon-linear crystal. The crystal length of the doubler crystal is howeverthen not optimised for frequency doubling so that where applicable theconversion efficiency for the second harmonic is unsatisfactory. Tooptimise the conversion efficiency for the second harmonic and for thegenerated sum frequency however an independent adaptation and henceoptimisation of the length of the two crystals is required.

[0023] According to the devices described in U.S. Pat. No. 5,835,513(Pieterse) and U.S. Pat. No. 5,848,079 (Kortz), run time differences inthe crystals for pulsed laser radiation are not influenced in a targetedmanner. The crystals are selected only by fulfilment of the phaseadaptation condition for the frequency conversion and the spatialoverlap of the beams in the second non-linear crystal being improved bythe walk-off generated in the first crystal. For crystal orientations tobe set for phase adaptation in the first and second crystal, thecorresponding dispersion would usually lead to a difference in the groupspeed for pulsed beams so that because of the associated run timedifferences, the temporal overlap of the light pulses in the crystals isnot optimum and hence the conversion efficiency is reduced.

[0024] The devices described in the said publications have in common thefact that the walk-off is only reduced so the spatial overlap of thebeams is improved for an efficient frequency conversion. No teaching isdisclosed to compensate for run time differences or the targeted changeof temporal spacing between laser pulses which leads to an improvementin temporal overlap and hence an increase in the conversion efficiencyfor pulsed laser beams.

[0025] U.S. Pat. No. 5,852,620 (“Tunable time plate”, Chaozhi Wan)describes an arrangement with which a continuous temporal delay can beset between two pulsed laser beams of pico-and femto-second duration.This comprises one or more double refracting crystals which aresupported rotatably. By rotating the crystal about a particular axis,the angle of incidence of the pulses relative to the optical axischanges. This changes the refractive index and the dispersion. Thisleads to a change in run time of the pulses through the crystal. Thespatial walk-off between the beams is not influenced in a targetedmanner in this process, so the conversion efficiency is reduced becauseof the walk-off. This publication gives no information on the spatialwalk-off associated with the selected irradiation direction. No teachingis given in this publication on compensation for the spatial walk-offand the improvement in conversion efficiency which can be achieved inthis way.

OBJECT

[0026] The object of the invention is to increase the conversionefficiency in optically non-linear frequency conversion in which atleast two pulsed laser beams are irradiated into an optically non-linearmedium, in particular an optically non-linear crystal, with simplemeans.

[0027] According to the invention, to increase the conversion efficiencyof optically non-linear conversion processes in which two pulsed laserbeams are irradiated into an optically non-linear medium e.g. a crystal,a double refracting crystal is arranged before this optically non-linearmedium. This double refracting crystal, referred to below as acompensator, has the property of improving both the spatial and thetemporal overlap of the light pulses irradiated into the non-linearcrystal. This is achieved by a suitable orientation of the optical axisof the compensator to the propagation direction of the laser pulses anda suitable compensator length. With the compensator the conversionefficiency of the optically non-linear frequency conversion method isincreased in comparison with the conversion efficiency withoutcompensator. The compensator according to the invention gives the pulsesin the two laser beams a temporal offset so that the pulses of the twobeams can reach preferably the centre of the frequency conversion medium(e.g. crystal) at the same time. The compensator in this case mustcompensate for the temporal offset, which arises between the pulses whenpassing through half the length of the frequency conversion mediumbecause of the different group speeds, and also compensate for thetemporal offset of the two pulses which they would have without acompensator according to the invention at the inlet facet of thefrequency conversion medium. The compensator according to the inventionmust also have the property that it compensates for the spatialseparation of the pulses via the spatial walk-off in the frequencyconversion medium. For this after passing through the compensator thelight pulses must be offset spatially by a distance which preferablycorresponds to half the spatial offset of the two beams after passingthrough the frequency conversion crystal. The compensator must bearranged so that the direction of the spatial offset in the compensatoris opposite the direction of the spatial offset in the frequencyconversion crystal.

[0028] The length of the compensator and orientation of the optical axisof the compensator to the propagation direction of the laser beams aredetermined by calculating the optical paths and the spatial separationof the pulses which are irradiated into the compensator as ordinary andextraordinary beams. The run times through the crystals and thecompensator are calculated via the group speeds of the light pulses andthe run distances using the refractive indices and dispersion data. Thesame applies to the run times in all optical elements through which thebeams pass. The spatial separation caused by the walk-off is calculatedusing the refractive indices and dispersion data of the opticallynon-linear crystals and compensator. The compensator is thus designed sothat the pulses irradiated into the compensator leave this with acertain spatial and temporal interval. The prespecified spatial andtemporal interval must be set at the same time by a suitable choice ofcrystal length and orientation of the optical crystal axis to thepropagation direction of the laser beams.

[0029] The particular advantage of this preferred embodiment of theinvention is that with a single element, the compensator, the temporaland spatial offsets of the light pulses can be influenced simultaneouslyin a targeted manner in the subsequent optically non-linear conversioncrystal or crystals, and adjusted with a view to improved conversionefficiency.

[0030] A further advantage of the invention is the fact that for twosuccessive non-linear processes the conversion efficiency for bothsingle processes can be optimised separately as the possible spatial andtemporal offset via the first conversion process can be influenced bythe compensator such that the resulting spatial and temporal offsetgives an improved efficiency for the second conversion process. Afurther advantage is that only one crystal is required for compensation.This does not participate in the optically non-linear conversion processitself and is also positioned in front of the conversion crystal. Thisis particularly advantageous if the conversion generates short-waveradiation in the conversion crystal. The compensator through which theshort wave radiation does not pass must therefore be transparent onlyfor the irradiated beams with longer wavelengths. This gives a widerselection of materials for the compensator. This is advantageous also inrelation to the facets of the compensator through which the laser beamspass, as any anti-reflection coatings applied there also need not bedesigned for short-wave radiation.

[0031] The freedom of choice of material for the compensator is all thelarger as the compensator itself does not participate in the opticallynon-linear process and hence is subject to no restrictions with regardto crystal orientation necessary for phase adaptation. A furtheradvantage is that the compensation can also be carried out in opticallynon-linear processes with a large spatial walk-off. There is norestriction from the possible refraction of the beams on the surface ofthe conversion crystal and the associated change in propagationdirection.

[0032] It is further advantageous that the compensator need not beintroduced in areas of focussed beams but a position can be selected atwhich the focal points of the beams are comparatively large. As a resultthe power densities are relatively low, so the load on the compensatorfrom the laser beam is far removed from its breaking limit. This reducesthe danger of destruction of the crystal from high laser power.

[0033] A further advantage is the low adjustment sensitivity of thecompensator. The angle setting in comparison with a crystal with phaseadaptation has a great tolerance. Therefore only a simple holder deviceis required for the compensator, which reduces the equipment costaccordingly.

[0034] It is also advantageous that the beams can strike the facets ofthe compensator and subsequent non-linear crystal perpendicular. Thisavoids the astigmatism which arises with non-perpendicular incidence.Thus no devices are required to compensate for astigmatism, whichfurther reduces the equipment cost.

[0035] The device according to the invention is now explained withreference to the following embodiment examples. The drawings show

[0036]FIG. 1: A device for frequency doubling with non-critical phaseadaptation and subsequent phase tripling with type II phase adaptation;

[0037]FIG. 2: A device for frequency doubling with non-critical phaseadaptation and subsequent phase tripling with compensator according tothe invention before the non-linear crystal for frequency tripling;

[0038]FIG. 3: A device for frequency tripling with compensator accordingto the invention and non-linear crystal for frequency tripling withangled outlet facet;

[0039]FIG. 4: A device for frequency conversion with a splitcompensator;

[0040]FIG. 5: A device for frequency conversion with critical phaseadaptation and subsequent frequency conversion with type II phaseadaptation, and

[0041]FIG. 6: A device for a frequency conversion with critical phaseadaptation and compensator according to the invention before thenon-linear crystal for frequency conversion with type II phaseadaptation.

[0042]FIG. 1 shows an arrangement as is normally used for frequencytripling. It comprises an arrangement for non-critical frequencydoubling and an arrangement for sum frequency mixing of fundamental andfrequency-doubled radiation. This arrangement contains a crystal (26)for frequency doubling and a crystal (56) for frequency tripling. Thelaser beam (14) has a linear polarisation (34). Using the optical device(22) the laser beam (14) is irradiated into the frequency doublercrystal (26). The optical device (22) irradiates such that a focus isformed in the crystal (26) to increase the power density of the laserbeam (14). The polarisation of the laser beam (14) is linear, the vectorof the electrical field is perpendicular to the plane of the diagram(1). The non-doubled beam (14) and the frequency-doubled beam (16) leavethe frequency doubler crystal (26). The frequency-doubled beam (16) hasa polarisation direction (36) which is orthogonal to the polarisationdirection (34) of the laser beam (14). If the frequency doubling usingthe frequency doubler crystal (26) is non-critical, the laser beam (14)and the frequency-doubled beam (16) are collinear. Because of thedispersion in the crystal (26), the group speeds of the two beams in thecrystal (26) are different. For pulsed laser radiation this gives atemporal offset between the pulses of the laser beam (14) and the pulsesof the frequency-doubled beam (16). The temporal offset is characterisedby points A and B. The pulse of the laser beam at a given time is atpoint B, the associated frequency-doubled pulse in contrast is only atpoint A. The temporal order of the pulses can also be reversed if thedispersion of the frequency doubler crystal is such that the group speedof the frequency-doubled beam (16) is greater than the group speed ofthe beam (14). The important factor is not the order but the differencein group speeds for laser and frequency-doubled pulses which leads to atemporal offset Δt of the pulses so that after the frequency doublercrystal the pulses are not at the same point at a given time.

[0043] Using the optical device (46) the laser pulses (14) and thefrequency-doubled pulses (16) are irradiated into the sum frequencymixed crystal (56) to generate the third harmonic. Because of thewalk-off of the frequency-doubled beam, this leaves the tripler crystalat point E. The fundamental beam which undergoes no walk-off leaves thetripler crystal at point D. The third harmonic (18) also leaves thetripler crystal at point D. The frequency-doubled beam (16) runs alongline CE, the fundamental beam along line CD. The optical device (72)focuses and forms the beam (18). This can be a lens, a lens system or asystem of reflective optics. Using the separator (74), the beams (14),(16) and (18) are separated. For this a wavelength-dependent and/orpolarisation-dependent selection of the beams is made with known opticalelements. These are in particular coated mirrors, prisms or polarisers.A combination of these elements for beam separation is also possible.

[0044] The group speeds of the laser pulses (14) and the pulses of thefrequency-doubled beam (16) are different in the non-linear crystal (26)and the focussing element (46). For this reason pulses (14) and (16)reach the non-linear crystal (56) at point C of the facet at differenttimes.

[0045] Because of the walk-off between the beams (14) and (16) in thecrystal (56), for beam diameters and crystal lengths common in practicethe spatial overlap of these beams while passing through the crystal islimited to a fraction of the crystal length.

[0046] Due to the reduced temporal and spatial overlap the conversionefficiency for generating the third harmonic in the crystal (56) isgreatly reduced.

[0047] The device according to the invention substantially improves thetemporal and spatial overlap. As a result the conversion efficiency isimproved. As the embodiment example described below shows, a deviceaccording to the invention can more than double the conversionefficiency.

[0048] The device according to the invention will be described using thestructure of FIG. 2.

[0049] In the beam path between the frequency doubler (26) and thefrequency tripler (56) is inserted the compensator (54) according to theinvention. The laser beam (14) runs via path F, H, K, L. Thefrequency-doubled beam runs via path F, G, J, L. The two beams meetpreferably in the centre of the tripler crystal (56). The direction ofthe walk-off in the compensator is set so that it is opposite thedirection of the walk-off in the tripler crystal. This enlarges thespatial overlap in the tripler crystal.

[0050] The spatial offset HG between the laser beam and thefrequency-doubled laser beam is given by:

HG=tan(ρ_(komp))·L _(komp)

[0051] Here ρ_(komp) is the walk-off angle of the extraordinary beam inthe compensator and L_(komp) the length of the compensator.

[0052] This offset is set so that distance JK on the facet of thetripler crystal preferably corresponds to half the distance DE (FIG. 1).Distance HG is equal to distance JK when the facets of the compensator(54) and frequency conversion crystal (56) are perpendicular to thelaser beam direction. To adjust the offset, the walk-off in thecompensator and the length of the compensator crystal are selectedsuitably. The walk-off angle is determined by the choice of propagationdirection of the laser beam (14) relative to the optical crystal axis ofthe compensator (54).

[0053] The orientation of the optical axis of the compensator and itslength are also selected so that the run time differences of the laserpulses and the pulses of the frequency-doubled beam in crystal (26) arecompensated in the focussing element (46) and in the tripler crystal(56) (on paths KL and JL). Thus the pulses of beams (14) and (16) reachpoint L at the same time. For this the group speed of thefrequency-doubled pulses in the compensator must be greater than thegroup speed of the pulses of the laser beam in the compensator as thefrequency-doubled beam has a longer path and has already undergone atemporal delay in relation to the laser beam due to the frequencydoubling.

[0054] By arranging a compensator before the crystal (56), firstlydistance KJ is set so that the beams physically meet at point L. At thesame time the temporal interval of the pulses of the two beams is set sothey reach point L at the same time. The compensator thus generates animproved spatial and temporal overlap in the tripler crystal.

[0055] With the length of the compensator and the orientation of itscrystal axis to the propagation direction of the laser beams, twoparameters are available which can be selected so that the said spatialand temporal conditions for improved beam overlap are fulfilledsimultaneously.

[0056] A further embodiment of the device according to the invention isshown diagrammatically in FIG. 3. In all figures components with thesame or similar function have the same reference numerals so a repeateddescription can be omitted.

[0057] In this embodiment the outlet facet (58) of the non-linearfrequency conversion crystal (56) is designed so that the beams (14),(16) and (18) leave the crystal in different directions. Then the beamseparation device (74) can be omitted. If the outlet facet (58) for thebeam (18) is cut at the Brewster angle, the beam leaves the crystalloss-free. For this the Brewster angle must be calculated for thepolarisation and wavelength of the beam (18).

[0058] A further embodiment is shown diagrammatically in FIG. 4.

[0059] In FIG. 4 to the left of the compensator should be added thecorresponding components according to FIG. 3 or 2. The compensator (54)is divided into two halves (54 a) and (54 b). The outlet side of thepart compensator (54 a) is cut at an angle to the beam direction. Theinlet side of the part compensator (54 b) has the same cut angle. Thetwo part compensators are oriented in relation to each other so thatthey would act as a compensator if the outlet side of part compensator(54 a) and the inlet side of part compensator (54 b) were placed againsteach other. If one of the two part compensators is firmly attached inthe beam path and the other part compensator is moved in the directionperpendicular to the beam path, the temporal compensation can becontinuously adjusted as the paths for the beams are changedcontinuously. The spatial beam offset generated by the compensator (54)is not changed as a result. In order to obtain the same spatial offsetof a single compensator (54) using two part compensators (54 a) and (54b), the refraction of the beam (16) at the outlet side of the partcompensator (54 a) and the inlet side of the part compensator (54 b)must be taken into account as due to the refraction an additionalspatial offset occurs. This depends on the cut angle of the partcompensators and the spacing of the part compensators, and can easily becalculated.

[0060]FIG. 5 (still without compensator) shows a case of frequencyconversion in which a walk-off is already present in the firstnon-linear crystal (26). This walk-off occurs for example on frequencyconversion with critical phase adaptation. After passing through thecrystal (26), the beams are separated by distance BC. The pulses ofbeams (14) and (16) are also temporally separated as at a given time thepulses in beam (14) are at point (103) and those of beam (16) have onlyreached point (101). The beams enter the second non-linear crystal (56)with temporal offset at points D (beam (14)) and F (beam (16)). Thewalk-off in crystal (56) leads to a deflection of the beam (16) so thatthis leaves the crystal (56) at point G. For this case too thecompensator according to the invention compensates for the spatial andtemporal offset of the pulses. This is shown in FIG. 6.

[0061] The favourable effect of the compensator is not restricted to afrequency conversion with type II phase adaptation after thecompensator. If the subsequent frequency conversion takes place withtype I phase adaptation, between the compensator (54) and frequencyconversion crystal (56) is inserted a half-wave plate for one of the twolaser beams entering the conversion crystal. This rotates thepolarisation direction of this beam through 90°, while the polarisationdirection of the other laser beam entering the conversion crystalremains unchanged. Thus the two laser beams in the conversion crystal(56) are polarised in the same direction.

[0062] As is clear from FIG. 6, the compensator must be designed inlength and cut angle so that the pulses of beams (14) and (16) meetpreferably in the centre of the non-linear crystal (56) at the sametime.

[0063] The advantages of the method according to the invention and thecorresponding device are shown by the following embodiment example. Thisconcerns a frequency tripling of a mode-coupled Nd:YVO₄ ultra-shortpulse laser.

EMBODIMENT EXAMPLE Frequency Tripling of a Mode-Coupled Nd:YVO₄ Laser

[0064] To generate the third harmonic of a mode-coupled ND:YVO₄ laserwith a fundamental wavelength of 1064 nm, the frequency-doubledradiation with a wavelength of 532 nm is generated in lithium triborate(LBO). The frequency doubling is of type I, i.e. the polarisation of thegenerated second harmonic is perpendicular to the polarisation of thefundamental wave. The LBO crystal has a x-cut, i.e. the y and z mainaxes of the crystal are oriented perpendicular to the beam direction.The LBO is operated at a temperature of around 150° C., where thefrequency doubling is non-critical without a spatial walk-off betweenthe fundamental wave and the frequency-doubled wave. The two beams runcollinear in the LBO crystal and after emerging from the LBO crystal.The group speeds of the 1064 nm pulse and the 532 nm pulse are differentin the LBO crystal because of dispersion. This gives a temporal offsetbetween two pulses which can be calculated using the known dispersiondata of LBO. For the non-critical frequency doubling there is a delay of44 fs per mm crystal length. After the frequency doubler, with an LBOcrystal length of 15 mm, the pulses are temporally offset to each otherby 660 fs. As the group speed of the 1064 nm pulse is greater than thatof the 532 nm pulse, the 532 nm pulse is delayed by 660 fs in relationto the 1064 nm pulse.

[0065] For frequency tripling, after the frequency doubler crystal anLBO crystal with critical phase adaptation is used: the crystal has thecut angle phi=90° and theta=42.5° for a crystal temperature of 25° C.The fundamental beam and the third harmonic are ordinarily polarised forthis crystal orientation, the frequency-doubled radiation isextraordinarily polarised. For this critical phase adaptation there is aspatial walk-off between the beams irradiated into the frequency triplercrystal. The walk-off between the 1064 nm beam and the 532 nm beam isρ=9.3 mrad (0.53°). The beams entering the tripler crystal collinearwill after the LBO crystal have a spatial offset of tan(ρ).L. Thespatial offset for the tripler crystal of length L=15 mm is 139 μm.

[0066] The group speed difference of the two pulses in the LBO triplercrystal is 219 fs/mm. For a 15 mm long crystal, the pulses have atemporal offset of 3.3 ps. Thus the 532 nm pulse, because of the lowergroup speed, will be delayed in relation to the 1064 nm pulse. Fordoubling and tripling, focussing in the non-linear crystal is required.The focus is selected so that it lies in the centre of the crystalconcerned. In the focus of the tripler crystal the pulses therefore havea temporal offset of 3.3/2=1.65 ps. For tripling, the overlap of thepulses and hence the conversion efficiency is greatest if the pulsesreach the focus at the same time. Therefore in total a temporalcompensation must be created which corresponds to the sum of thetemporal offset on passing through the doubling crystal and the temporaloffset on passing through half the crystal length of the triplercrystal. The temporal offset from the optical device (46) is negligiblein this embodiment example because of the low offset. In total thus atemporal offset of 2.31 ps must be compensated.

[0067] To compensate for the spatial walk-off and temporal offset,according to the invention as a compensator a double refracting BBOcrystal is positioned before the tripler crystal. The BBO hasanti-reflective coated surfaces which minimise the losses for 1064 nmand 532 nm. In accordance with the statements for the compensator, forthe BBO crystal a cut angle is achieved of 86.35°. The crystal must thenhave a length of 8 mm.

[0068] The mode-coupled Nd:YVO₄ laser has a pulse length of 9 ps and amean power of 18 W for a wavelength of 1064 nm. When the compensator isused a third harmonic power is generated of 4 W at 355 nm. If thecompensator is not used the power is just 1.5 W. The conversionefficiency is thus more than doubled by the compensator.

[0069] If the compensator has a crystal angle of 90° and is introducedperpendicular into the beam path, with this compensator only thetemporal offset can be compensated since for this crystal orientationthere is no spatial walk-off in the compensator. If such a crystal isused as a compensator in frequency tripling, the power of the thirdharmonic is 2.2 W. It is as expected higher than the power withoutcompensator but lower than the power with the compensator whichcompensates for both the temporal and the spatial offset.

[0070] For compensation not only BBO can be used. Examples of othersuitable double refracting crystals are KDP, YVO₄, BiBO₃ and quartz.E.g. for the embodiment example of frequency tripling with a compensatorof KDP, there is an angle of 86.8° and a length of 23.2 nm. The saidcrystals are not the only ones possible, the person skilled in the artusing the calculation specifications given can easily calculate thenecessary orientation angle and length of the crystal concerned also forother double refracting crystals.

1. A device for optical frequency conversion of at least two laser beams(14, 16) of ultra-short beam pulses which have a temporal offset and aspatial walk-off, with at least one optically non-linear medium (56),comprising: in the beam path before the optically non-linear medium (56)is arranged a double refracting crystal (54), the length of which andthe optical crystal axis of which to the propagation direction of thelaser beam are set such that the change caused by the double refractingcrystal (54) in the location and time of incidence of the beam pulses(14, 16) on the optically non-linear medium (56), the direction of thewalk-off in the double refracting crystal (54) being opposite thedirection of the walk-off in the optically non-linear medium (56), andthe resulting change in the spatial and temporal overlap of the beampulses in the optically non-linear medium (56) for optical frequencyconversion in the medium (56) give a conversion efficiency which ishigher than the conversion efficiency which would be achieved withoutthe double refracting crystal (56).
 2. The device according to claim 1,wherein a first (14) of the at least two laser beams (14, 16) is thefundamental beam from an ultra-short pulse laser and a second (16) ofthe at least two laser beams (14, 16) is the second harmonic of thefirst laser beam (14) which is generated in an optically non-linearcrystal (26) by means of non-critical phase adaptation.
 3. The deviceaccording to claim 1, wherein a first (14) of the at least two laserbeams (14, 16) is the fundamental beam from an ultra-short pulse laserand a second (16) of the at least two laser beams (14, 16) is the secondharmonic of the laser beam (14) which is generated in an opticallynon-linear crystal (26) with critical phase adaptation.
 4. The deviceaccording to claim 1, wherein the optically non-linear medium (56)generates beam pulses with the sum frequency of the frequencies of thelaser beams (14, 16).
 5. The device according to claim 1, wherein theoptically non-linear medium (56) generates beam pulses with thedifference frequency of the frequencies of the laser beams (14, 16). 6.The device according to claim 1, wherein the double refracting crystalcomprises BBO, KDP, KD*P, YVO₄, quartz, LBO or BiBO₃.
 7. The deviceaccording to claim 1, wherein the double refracting crystal (54) hasdouble refracting crystal components (54 a, 54 b), one (54 b) of thecrystal components being displaceable in relation to the other in orderto continuously adapt the run times of the laser beams (14, 16) throughthe double refracting crystal (54).
 8. The device according to claim 1,wherein the outlet facet of the optically non-linear crystal (56), usedto generate the sum or difference frequency, is not perpendicular to thepropagation direction of at least one of the three beams (14, 16, 18).9. The device according to claim 1, wherein the optically non-linearmedium (56) is a crystal.
 10. Method for optical frequency conversion ofat least two laser beams (14, 16) of ultra-short beam pulses which havea temporal offset and a spatial walk-off, and in at least one opticallynon-linear medium (56) undergo a non-linear frequency conversion,characterised in that before the optically non-linear medium (56) isarranged a double refracting crystal (54), the length of which and theorientation of the optical crystal axis of which to the propagationdirection of the laser beam are set such that the change caused by thedouble refracting crystal (54) in the location and time of incidence ofthe beam pulses (14, 16) on the optically non-linear medium (56), thedirection of the walk-off in the double refracting crystal (54) beingopposite the direction of the walk-off in the optically non-linearmedium (56), and the resulting change in the spatial and temporaloverlap of the beam pulses in the optically non-linear medium (56) foroptical frequency conversion in the medium (56) give a conversionefficiency which is higher than the conversion efficiency which isachieved without the double refracting crystal (54).
 11. Use of a doublerefracting crystal (54) in a device for optical frequency conversion ofat least two laser beams (14, 16) of ultra-short beam pulses which havea temporal offset and a spatial walk-off, and which generate a frequencyconversion in at least one optically non-linear medium (56), wherein thedouble refracting crystal (54) is arranged in the beam path before anoptically non-linear medium (56) such that its length and theorientation of its optically active crystal axis relative to thepropagation direction of the laser beams (14, 16) are such that thechange caused by the double refracting crystal (54) in the location andtime of incidence of the beam pulses (14, 16) on the opticallynon-linear medium (56), the direction of the walk-off in the doublerefracting crystal (54) being opposite the direction of the walk-off inthe optically non-linear medium (56), and the resulting change in thespatial and temporal overlap of the beam pulses in the opticallynon-linear medium (56) for optical frequency conversion in the crystal(56) give a conversion efficiency which is higher than the conversionefficiency which is achieved without the double refracting crystal (54).12. The device according to claim 2, wherein the double refractingcrystal comprises BBO, KDP, KD*P, YVO₄, quartz, LBO or BiBO₃.
 13. Thedevice according to claim 3, wherein the double refracting crystalcomprises BBO, KDP, KD*P, YVO₄, quartz, LBO or BiBO₃.
 14. The deviceaccording to claim 4, wherein the double refracting crystal comprisesBBO, KDP, KD*P, YVO₄, quartz, LBO or BiBO₃.
 15. The device according toclaim 5, wherein the double refracting crystal comprises BBO, KDP, KD*P,YVO₄, quartz, LBO or BiBO₃.
 16. The device according to claim 2, whereinthe double refracting crystal (54) has double refracting crystalcomponents (54 a, 54 b), one (54 b) of the crystal components beingdisplaceable in relation to the other in order to continuously adapt therun times of the laser beams (14, 16) through the double refractingcrystal (54).
 17. The device according to claim 16, wherein the outletfacet of the optically non-linear crystal (56), used to generate the sumor difference frequency, is not perpendicular to the propagationdirection of at least one of the three beams (14, 16, 18).
 18. Thedevice according to claim 17, wherein the optically non-linear medium(56) is a crystal.
 19. The device according to claim 1, wherein theoptically non-linear medium (56) is a crystal.
 20. The device accordingto claim 15, wherein the optically non-linear medium (56) is a crystal.